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K-extreme point of generalized orlicz sequence spaces with Luxemburg norm

100%

Shi Z.

Commentationes Mathematicae

2013

tom 53

nr 2

In this paper,we give necessary and sufficient conditions in order that a point $u\in S(l_{({\it \Phi})})$ is a k-extreme point in generalized Orlicz sequence spaces equipped with the Luxemburg norm, combing the methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between the classical Orlicz spaces and generalized Orlicz spaces.

Strongly exposed points in Musielak-Orlicz sequence spaces endowed with Orlicz norm

63%

Shi Z. , Liu C.

Banach Center Publications

2011

tom 92

nr 1

327-338

A criterion for strongly exposed points of the unit ball $B(l_{M})$ in Musielak-Orlicz sequence spaces $l_{M}$ equipped with Orlicz norm is given.

Some Structures Related to Metric Projections in Orlicz Spaces

63%

Lin B.-L. , Shi Z.

Colloquium Mathematicum

1999

tom 81

nr 2

223-235

We discuss k-rotundity, weak k-rotundity, C-k-rotundity, weak C-k-rotundity, k-nearly uniform convexity, k-β property, C-I property, C-II property, C-III property and nearly uniform convexity both pointwise and global in Orlicz function spaces equipped with Luxemburg norm. Applications to continuity for the metric projection at a given point are given in Orlicz function spaces with Luxemburg norm.

Orlicz sequence spaces that are uniformly rotund in a weakly compact set of directions

51%

Shi Z. , Wang Y. , Dong G.

Colloquium Mathematicum

2007

tom 107

nr 1

21-34

Necessary and sufficient conditions are given for Orlicz sequence spaces equipped with the Orlicz norm to be uniformly rotund in a weakly compact set of directions, using only conditions on the generating function of the space.